What is the relationship between mass and weight?

The relationship between mass and weight is fundamentally understood through the concept of gravity. Weight is the force exerted by gravity on an object, and it is directly proportional to the object's mass. This means that as the mass of an object increases, its weight also increases, assuming the gravitational force remains constant. The formula that represents this relationship is weight (W) = mass (m) × gravitational acceleration (g), where gravitational acceleration is approximately 9.81 m/s² on the surface of the Earth.

Understanding this relationship is crucial in various engineering and physics applications, as it helps in calculating loads, forces, and designing structures. This connection highlights that weight cannot exist without mass, but mass itself is a measure of the amount of matter in an object and does not change regardless of location, provided that the object remains in a uniform gravitational field. Definitions of mass and weight encompass their interdependence while illustrating that mass is a scalar quantity, and weight is a vector quantity affected by gravitational forces.